Interference Mitigation & Massive MIMO for 5G - A Summary of CPqDs Results
5G Multimedia Massive MIMO Communications...
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WIRELESS COMMUNICATIONS AND MOBILE COMPUTING
Wirel. Commun. Mob. Comput. 0000; 00:1–14
DOI: 10.1002/wcm
RESEARCH ARTICLE
5G Multimedia Massive MIMO Communications SystemsXiaohu Ge1, Haichao Wang1, Ran Zi1, Qiang Li1 and Qiang Ni2
1School of Electronic Information and Communications, Huazhong University of Science & Technology, Wuhan, China.2School of Computing and Communications, Lancaster University, Lancaster LA1 4WA, UK.
ABSTRACT
In the Fifth generation (5G) wireless communication systems, a majority of the traffic demands is contributed by
various multimedia applications. To support the future 5G multimedia communication systems, the massive multiple-input
multiple-output (MIMO) technique is recognized as a key enabler due to its high spectral efficiency. The massive antennas
and radio frequency (RF) chains not only improve the implementation cost of 5G wireless communication systems but also
result in an intense mutual coupling effect among antennas because of the limited space for deploying antennas. To reduce
the cost, an optimal equivalent precoding matrix with the minimum number of RF chains is proposed for 5G multimedia
massive MIMO communication systems considering the mutual coupling effect. Moreover, an upper bound of the effective
capacity is derived for 5G multimedia massive MIMO communication systems. Two antenna receive diversity gain models
are built and analyzed. The impacts of the antenna spacing, the number of antennas, the quality of service (QoS) statistical
exponent, and the number of independent incident directions on the effective capacity of 5G multimedia massive MIMO
communication systems are analyzed. Comparing with the conventional zero-forcing precoding matrix, simulation results
demonstrate that the proposed optimal equivalent precoding matrix can achieve a higher achievable rate for 5G multimedia
massive MIMO communication systems. Copyright c⃝ 0000 John Wiley & Sons, Ltd.
KEYWORDS
mutual coupling, massive MIMO systems, effective capacity, RF chains, equivalent precoding.
∗Correspondence
Dr. Qiang Li, School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan
430074, Hubei, P. R.China. E-mail: qli [email protected]
Part of this work appeared in the IEEE IWCMC 2015 [1], which was granted the best paper award.
1. INTRODUCTION
As various wireless multimedia applications are getting
more and more popular, the demand for wireless traffic
is increasing rapidly, and the massive multi-input-multi-
output (MIMO) technology has been proposed as a
key technology for the next generation (5G) wireless
communication systems [2–4], facilitating to guarantee the
increasing demand of user QoE (Quality of Experience)
[5, 6]. Recently, a number of excellent studies have
validated that massive MIMO systems are specialized in
improving the wireless communication capacity vastly in
cellular networks[7]. Apparently the huge antenna arrays
have to be deployed compactly because enough space
are not available at not only base stations (BSs) but
also mobile terminals, therefor the interaction of mutual
coupling among antennas gets so strong that it can’t be
ignored in massive MIMO systems[8]. Also, the realistic
channel capacity which is subject to the quality of service
(QoS) in multimedia wireless communication systems and
the Shannon capacity are not the same thing [9–12]. So,
Copyright c⃝ 0000 John Wiley & Sons, Ltd. 1
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5G Multimedia Massive MIMO Communications Systems Xiaohu Ge et al.
exploring a new precoding solution for the 5G massive
MIMO multimedia communication systems is necessary.
A lot of studies have achieved great achievements
about mutual coupling among multiple antennas on many
topics such as antenna propagation, signal processing and
antenna arrays [13–16]. Utilizing the real measurement
data, the authors of [13] have made a comparison on
the antenna array performance between the systems
considering the mutual coupling and the systems not. It
has been proved that mutual coupling has a great influence
on the performance of antenna arrays for not only small
but also large inter-antenna spacing, because that in order
to contain the changes in all the anticipant vectors, the
steering vectors of the antenna arrays should be adjusted
not only in amplitude but also in phase[14]. Clerckx et.
al. studied how the mutual coupling influenced a simple
multi-antenna communication system performance [15]. In
order to recover the signals received by separate antennas
without mutual coupling, the authors of [16] have invented
a new technique to make a compensation for mutual
coupling in small antenna arrays.
At practical wireless communication transmission
terminals, each data stream is first passed through the
baseband precoding to radio frequency (RF) chains and
then is transmitted to antennas by the RF chains precoding.
For MIMO wireless systems, the precoding technologies
are focused on the baseband precoding, i.e., the first
order precoding, and each RF chain corresponds to an
antenna. Utilizing the phase matrix between RF chains and
antennas, the joint precoding of baseband and RF chains
was proposed for massive MIMO systems with limited
RF chains [17, 18]. However, it is still a great challenge
to reduce the number of RF chains for saving the cost of
massive MIMO wireless communication systems.
Lots of excellent studies in the field of wireless
multimedia communication have emerged [19–23]. In
order to evaluate the QoS of wireless multimedia networks,
the authors in [19, 20] created a constrained model of
statistical QoS to study the transmission characteristics
of data queues. In [21, 22], the authors referred to the
effective capacity of the block fading channel model and
proposed a rate and power adaption scheme in which
the power is driven by QoS. And in [23], the authors
further combined the effective capacity with information
theory and developed some rate adaptation and QoS-
driven power schemes which were suitable for the systems
of multiplexing and diversity. Also they concluded that
stringent QoS and high throughput can be achieved by
the multi-channel communication systems simultaneously
according to their simulation results. However, rare
efforts has been made to study the effective capacity
of massive MIMO multimedia wireless communication
systems which consider the QoS constraint and mutual
coupling effect.
Motivated by the above gaps, we propose an optimal
equivalent precoding matrix to reduce the cost of RF chains
in 5G massive MIMO multimedia communication systems
and derive the upper bound of effective capacity with QoS
constraints. The main contributions of this paper are listed
as follows.
1. We define the receive diversity gain to analyze
how the mutual coupling influence the performance
of the rectangular antenna arrays in the massive
MIMO wireless communication systems.
2. An optimal equivalent precoding matrix is proposed
to reduce the cost of RF chains and satisfy
the multimedia data requirements for 5G massive
MIMO multimedia communication systems.
3. We refer to the QoS statistical exponent constraint
and the mutual coupling effect, then derive the
upper bound of effective capacity for 5G massive
MIMO multimedia communication systems.
4. Based on numerical results, the proposed optimal
equivalent precoding matrix is compared with the
conventional zero-forcing (ZF) precoding matrix
in 5G massive MIMO multimedia communication
systems.
The rest of this paper is summarized as follows.
In Section 2, a system model in which there is a
2D antenna array is described for massive MIMO
wireless communications. In Section 3, the effect of
mutual coupling on the massive MIMO wireless systems
is evaluated by the receive diversity gain. Moreover,
an optimal equivalent precoding matrix is proposed
to reduce the cost of RF chains and satisfy the
multimedia data requirements for 5G massive MIMO
multimedia communication systems. Furthermore, the
upper bound of effective capacity is derived for 5G massive
MIMO multimedia communication systems. Numerical
simulations and analysis are presented in Section 4.
Finally, Section 5 summarizes the paper.
2 Wirel. Commun. Mob. Comput. 0000; 00:1–14 c⃝ 0000 John Wiley & Sons, Ltd.
DOI: 10.1002/wcm
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User
Equipment(UE)
Scatters
Base station with
an antenna array
λ : Wave length
aλ: array length
bλ: array width
d : antenna
distance
R : distance
between the UE
and the BS
antenna array
1 2 3 . . . m
bλ
aλ
n antenna
elements
m antenna
elements
1
2
.
.
.
n
R
d
d
Figure 1. System model.
2. SYSTEM MODEL
A massive MIMO wireless transmission system is
illustrated in Fig. 1. The wireless down-link between a user
equipment (UE) with multi-antenna and a BS with a 2D
rectangular antenna array is studied in this paper.
First of all, we define some basic parameters for this
model. We define λ as the wavelength of the carrier, d as
the antenna spacing of this antenna array, aλ (a ≥ 1) as the
length of this antenna array and bλ (b ≥ 1) as the width of
this antenna array. If we would like to deploy m antennas
in each row and n antennas in each column for this antenna
array, then we will have the relationship as listed in (1),
d =aλ
m− 1=
bλ
n− 1, (1)
and the total number of antennas in this antenna array M
can be derived easily as
M = mn. (2)
If we define SNRBS as the signal-to-noise ratio (SNR)
at the BS, H and β stand for the small scale fading matrix
and large scale fading coefficient of the channel in this
model respectively, the signal the BS transmits is defined
as x, w means the additive white Gaussian noise (AWGN)
over wireless channels, and the mutual coupling matrix is
configured as K, equivalent precoding matrix is configured
as Feq , A is defined as steering matrix, then the down-link
signal vector received at a UE equipped with N antennas
can be expressed as
y =√SNRBSHAKFeqβ
1/2x+w, (3)
in which x is a Ns × 1 vector, w is a N × 1 vector.
H ∼ CN (0, P I) is governed by a complex Gaussian
distribution, and is expressed as
H = [h1, ...,hp, ...,hP ]T ∈ CN×P , (4)
in which CN×P denotes a N × P matrix, P stands for
the number of the independent incident directions, hp ∼CN (0, I) stands for the complex coefficient vector of
small scale fading received from the pth incident direction,
which is expressed as
hp = h(r)p + jh(i)
p , (5)
in which h(r)p is defined as the real part of hp, and h
(i)p
is defined as the imaginary part of hp. Furthermore,
both of them are Gaussian random variables distributed
independently and identically, whose expectation and
variance are 0 and 0.5 respectively.
Definitely, P will be very large if considerable scatterers
exist in the propagation environment. According to [24,
25], we divide the angular domain into P independent
incident directions with P being large but finite.
Here we assume both of the azimuth angle ϕq(q =
1, ..., P ) and elevation angle θ are within the scope
of [−π/2, π/2]. Each independent incident direction
corresponds to one steering vector a (ϕq, θ) ∈ CM×1, so
all the P steering vectors can constitute the steering matrix
A of the rectangular antenna array which is expressed as
A = [a (ϕ1, θ) , ..., a (ϕq, θ) , ..., a (ϕP , θ)] . (6)
If we define Aq ∈ Cn×m as the steering matrix of the qth
incident direction of the rectangular antenna array, we will
get the following relationship,
vec (Aq) = a (ϕq, θ) , (7)
in which vec (·) is defined as the matrix vectorization
operation.
Without loss of generality, we assume the antenna which
locates at the first place for both the row and the column
of the rectangular antenna array as the reference point
of which the phase response is zero. And we normalize
amplitude responses of all the antennas of the antenna
array as 1. We define Aqce, (1 ≤ c ≤ m, 1 ≤ e ≤ n) as the
element in the steering matrix Aq which locates at the cth
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5G Multimedia Massive MIMO Communications Systems Xiaohu Ge et al.
row and eth column, and it is expressed as
Aqce = exp
j2π
λ
(c− 1)dcosϕqsinθ
+(e− 1)dsinϕqsinθ
. (8)
For a rectangular antenna array with M elements, we
define K ∈ CM×M as the corresponding mutual coupling
matrix, which is expressed as [15]
K = ZL(ZLI+ ZM )−1, (9)
in which ZL denotes the antenna load impedance that
is constant for each antenna, ZM denotes the M ×M
mutual impedance matrix, and I denotes an M ×M
unit matrix. From Fig. 1, ZM can be constructed by
n× n sub-matrices, i.e.,ZM = [Zst]n×n, where Zst, as
an m×m mutual impedance sub-matrix, denotes the
mutual impedances between the m antennas located at
the sth (s = 1, ..., n) row and the m antennas located
at the tth (t = 1, ..., n) row in the rectangular antenna
array. For ease of exposition, we define Antsu as the
antenna located at the sth row and uth (s = 1, ...,m;u =
1, ...,m) column of the rectangular antenna array, and
define Anttv as the antenna located at the tth row and the
vth (t = 1, ...,m; v = 1, ...,m) column of the rectangular
antenna array, the corresponding distance between which
is given as dstuv = d√
(t− s)2 + (v − u)2. Thus Zst can
be written as
Zst =
zst11 zst12 ... zst1m
zst21 zst22 ... zst2m...
.... . .
...
zstm1 zstm2 ... zstmm
, (10)
Consider a special case where all M antenna elements
in the rectangular antenna array are dipole antennas with
the same parameters. Then the mutual impedance zstuv only
depends on the antenna spacing and can be obtained with
the EMF method in [32]. With a fixed antenna spacing d,
we have the following properties:
zstuv = zst(u+1),(v+1), (11)
zstuv = zstvu. (12)
Similar properties can be derived for Zst as
Zst = Z(s+1),(t+1), (13)
Zst = Zts. (14)
Together with (10)-(14), the mutual impedance matrix
ZM can be readily obtained. It bears noting that with (10)-
(14), the computational complexity can be significantly
reduced compared to the direct calculation of the M ×M
entries of ZM , especially with a large M .
The equivalent precoding matrix Feq = FRFFBB con-
sists of baseband precoding matrix FBB and the RF
precoding matrixFRF .
Ns data streams are transmitted by N tRF radio
frequency (RF) chains and M antennas at the BS. All
wireless data is received by NrRF RF chains and N
antennas at the UE. In this case, the detected wireless
signals at the UE is expressed by
y = W†eqy = W†
BBW†RFy, (15)
in which † is a conjugate transpose operation, Weq is a
N ×Ns equivalent signal detection matrix which consists
of baseband detection matrix WBB and the RF detection
matrix WRF , y is the received signal vector at antennas
of the UE. Essentially, FRF and WRF are phase shift
matrices used for the signal precoding and detection at the
RF chains. Hence, the absolute value of the RF detection
matrix FRF and the RF precoding matrix FRF is equal to
1.
3. MUTUAL COUPLING EFFECTMODELING
3.1. Receive Diversity Gain Models
Deployed in a constrained space at the BS, the number
of antenna elements is inversely proportional to the
antenna spacing, i.e., a larger number of antennas lead to
a smaller antenna spacing. As concluded in [26], more
antennas lead to a higher receive diversity gain of the
massive MIMO system, whereas the diversity gain can be
compromised by the mutual coupling effect that is caused
by decreasing the antenna spacing. Thus, when a number
of antennas are deployed in a fixed constrained area, there
4 Wirel. Commun. Mob. Comput. 0000; 00:1–14 c⃝ 0000 John Wiley & Sons, Ltd.
DOI: 10.1002/wcm
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Xiaohu Ge et al. 5G Multimedia Massive MIMO Communications Systems
Rmax = log
∣∣∣∣I+ SNRBS
NsW†
eqHAKFeqF†eqK
†A†H†WeqR−1
∣∣∣∣ , (21)
withR = W†
eqWeq. (21.1)
exists a tradeoff between M and d, and it is important to
analyze the the effect of mutual coupling on the achievable
receive diversity gain of the massive MIMO systems.
Firstly, with a fixed antenna spacing, the antenna
number receive diversity gain GM is defined as
GM = ξdminM − ξdmin
Mmin, (16)
in which ξdminM denotes the expectation of the receive
SNR at the UE with M antennas and minimum antenna
spacing being dmin at the antenna array of the BS, and
ξdminMmin
denotes the expectation of the receive SNR at the
UE subject to the minimum antenna spacing dmin and
minimum antenna number Mmin at the antenna array of
the BS.
Secondly, with a fixed number of antennas, the antenna
spacing receive diversity gain Gd is defined as
Gd = ξdMmin− ξdmin
Mmin, (17)
in which ξdMmindenotes the expectation of the receive
SNR at the UE with an antenna spacing of d and with at
least Mmin antennas at the antenna array of the BS. ξdminMmin
,
which can be considered as the baseline for Gd and GM ,
is the same as that in (16).
In order to obtain the expectation of the received SNR in
(16) and (17), perfect channel state information is assumed
to be available at the BS, which uses maximal-ratio
combining (MRC) for signal detection. When there are M
antennas and the neighboring antennas are separated with
a spacing of d, the received signal after MRC detection at
the UE is given as [27]
y = G†y =√SNRUEG
†Gx +G†w, (18a)
in which G† denotes the conjugate transpose of G with
G = HAKFeqβ1/2. (18b)
In addition, the average SNR seen at the UE side can be
written as
SNRUE =SNRBS
∥∥G†G∥∥2
∥G†G∥
= SNRBS
∥∥∥G†G∥∥∥ , (19)
Then with M antenna elements with antenna spacing d,
the expectation of the SNR at the UE can be obtained as
ξdM = E {SNRUE}
= SNRBSE{∥∥∥G†G
∥∥∥}= SNRBSNβ
∥∥∥F†eqK
†A†H†HAKFeq
∥∥∥, (20)
in which E {·} denotes the expectation operation. We can
further obtain Gd and GM through substituting (20) into
(16) and (17), and replacing M and d with Mmin and dmin.
3.2. Shannon Capacity with Optimal RF Chains
A phase shift matrix is designed to separate the
RF chains and the antennas. Assume that the relation-
ship among the numbers of data stream, RF chains
and antennas is configured as Ns 6 N tRF 6 M . Con-
sidering the equivalent precoding matrix (Feq)M×Ns=
(FRF )M×NtRF
(FBB)NtRF
×Ns, about it’s rank, we have
rank (Feq) 6 min(Ns, N
tRF ,M
). This result implies
that the up-bound of the degree of freedom at the equiva-
lent precoding matrix is depended on the minimum among
the numbers of data stream, RF chains and antennas. When
the number of RF chains is larger than the number of data
stream, a part of number of RF chains, i.e., N tRF −Ns, has
not been utilized by the equivalent precoding matrix. To
save the cost, the number of RF chains can be configured as
Ns to satisfy the requirement of the equivalent precoding
matrix Feq .
Based on the system model in Fig. 1, the sys-
tem achievable rate, i.e., the maximum Shannon capac-
ity is expressed by (21) and normalized on the unit
bandwidth [28]. Let MIN = min (M,P ), the eigen-
values of wireless channels H are ordered by λ1 >
Wirel. Commun. Mob. Comput. 0000; 00:1–14 c⃝ 0000 John Wiley & Sons, Ltd. 5DOI: 10.1002/wcm
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5G Multimedia Massive MIMO Communications Systems Xiaohu Ge et al.
Rmax = log
∣∣∣∣I+ SNRBS
NsHFF†H†Weq
(W†
eqWeq
)−1
W†eq
∣∣∣∣= log
∣∣∣∣I+ SNRBS
NsUHΣHV†
HUFΣFΣ†FU
†FVHΣ†
HU†H
∣∣∣∣= log
∣∣∣∣I+ SNRBS
NsV†
HUFΣFΣ†FU
†FVHΣ†
HΣH
∣∣∣∣, (25)
λ2 · · · > λMIN . The maximum available rate is Rmax =MIN∑k=1
log(1 + SNRBS
Nsλk
), where SNRBS is the SNR
value at the BS. The rank of wireless channel H
is denoted by r = rank (H). As a consequence, the
maximum available rate is rewritten by Rmax full =rank(H)∑
k=1
log(1 + SNR BS
Nsλk
). When the numbers of data
stream and RF chains are equal to the rank of wire-
less channel rank (H), the wireless channel capacity has
been fully utilized. When the rank of wireless channels
rank (H) is less than the number of data stream, what
should we do to configure the number of RF chains? To
utilize the wireless channel capacity and save the imple-
mentation cost of RF chains, the number of RF chains is
configured as the rank of wireless channels in this paper.
To simplify the derivation, the rank of wireless channels
is assumed to be larger than the number of data stream
in the following study. The optimal equivalent detection
matrix Weq is derived by a singular value decomposition
(SVD) method
Weq = UWΣWV†W, (22)
with
ΣW =
∆W
0
, (22.1)
∆W =
w1 0 · · · 0
0 w2 · · · 0...
.... . .
...
0 0 · · · wr
, (22.2)
in which UW and V†W are unitary matrices.
The optimal equivalent precoding matrix Feq is derived
by a SVD method
Feq = UFΣFV†F, (23)
with
ΣF =
(∆F 0
0 0
), (23.1)
∆F =
f1 0 · · · 0
0 f2 · · · 0...
.... . .
...
0 0 · · · fr
, (23.2)
in which UF and V†F are unitary matrices.
When a SVD method is performed over the equivalent
channel Heq = HAK, the equivalent channel is derived
by
Heq = UHΣHV†H, (24)
with
ΣH =
(∆H 0
0 0
), (24.1)
∆H =
λ1 0 · · · 0
0 λ2 · · · 0...
.... . .
...
0 0 · · · λr
, (24.2)
in which UH and V†H are unitary matrices.
Based on (22), (23) and (24), the maximum available
rate Rmax is further derived by a SVD method in (25) when
the optimal equivalent detection matrix Weq is assumed to
be a non-singular matrix. Let
ΣF2 = ΣFΣ†F =
(∆F∆
†F 0
0 0
), (26)
ΣH2 = Σ†HΣH =
(Ơ
H∆H 0
0 0
), (27)
U = V†HUF. (28)
(25) is rewritten by
R = log
∣∣∣∣I+ SNRBS
NsUΣF2U†ΣH2
∣∣∣∣, (29)
6 Wirel. Commun. Mob. Comput. 0000; 00:1–14 c⃝ 0000 John Wiley & Sons, Ltd.
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Xiaohu Ge et al. 5G Multimedia Massive MIMO Communications Systems
Rmax = log
∣∣∣∣SNRBS
Ns
(Ns
SNRBSI+ΣF2ΣH2
)∣∣∣∣= r log
(SNRBS
Ns
)+ log
(r
Πi=1
(Ns
SNRBS+ f2
i λ2i
)), (32)
L(f21 , f
22 · · · f2
r
)=
(Ns
SNRBS+ λ2
1f21
)(Ns
SNRBS+ λ2
2f22
)· · ·(
Ns
SNRBS+ λ2
rf2r
)+α
(f21 + f2
2 + · · ·+ f2r −N2
s
) . (33)
∂L(f21 , f
22 · · · f2
r
)∂f2
i
= λ2i
(Ns
SNRBS+ λ2
1f21
)· · ·(
Ns
SNRBS+ λ2
i−1f2i−1
)×(
Ns
SNRBS+ λ2
i+1f2i+1
)· · ·(
Ns
SNRBS+ λ2
rf2r
)+ α
, (34)
in which ΣF2 and ΣH2 are diagonal matrices and the
values of elements at diagonal line are larger than zero.
Furthermore, the eigenvalues of ΣF2 and ΣH2 are the
elements at the diagonal lines, respectively. U is a unitary
matrix, i.e., ∥U∥2 = M . When U is configured as a
diagonal matrix, the maximum available rate is achieved
by
Rmax = log
∣∣∣∣I+ SNRBS
NsΣF2ΣH2
∣∣∣∣. (30)
Assume that the transmission power at the BSs is
independent of the equivalent precoding matrix. This
assumption implies that ∥Feq∥F = Ns, i.e.,
r∑i=1
f2i = N2
s . (31)
The maximum available rate Rmax can be simplified as
(32).
To achieve the maximum achievable rate, the optimal
solution of the equivalent precoding is derived by a
Lagrange multiplier method in the following. A function
is first constructed in (33) with Lagrange factor α. And
then take the derivative of L(f21 , f
22 · · · f2
r
)with respect
to f2i , (i = 1, 2...r) in (34).
Let∂L(f21 , f
22 · · · f2
r
)∂f2
i
= 0, (35)
in which (i = 1, 2...r), we can further derive the following
result
NsSNRBS
λ2i
+ f2i =
NsSNRBS
λ2j
+ f2j
⇒ f2i − f2
j =Ns
SNRBS
(1
λ2j
− 1
λ2i
), (36)
in which (i, j = 1, 2...r).
Based on (31), the square of eigenvalues at the
equivalent precoding matrix Feq is derived by
f2i =
Ns
(1λ21+ 1
λ22+ · · ·+ 1
λ2r
)SNRBSr
+N2
s
r− Ns
SNRBSλ2i
. (37)
According to (25) and (30), we know that Weq , VF,
UH and U are removed in the simplification process of
Rmax, so VF, UH and U can be unit matrices. And
furthermore, UF and VH can also be unit matrices, and
UF = VH. Considering the Weq is a N ×Ns non-
singular matrix, Weq can be decomposed by
Weq =
(I
0
), (38)
In this case, the optimal equivalent precoding matrix is
simplified byFeq = UFΣFV
†F
= VHΣF
. (39)
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Feq =
ejϑ1,1 · · · ejϑ1,2r 0 · · · 0... · · ·
...... · · ·
...ejϑM,1 · · · ejϑM,2r 0 · · · 0
︸ ︷︷ ︸
(FRF )M×2Ns
b1 0 · · · 0 0 · · · 0b1 0 · · · 0 0 · · · 00 b2 · · · 0 0 · · · 00 b2 · · · 0 0 · · · 0...
.... . .
...... · · ·
...0 0 · · · br 0 · · · 00 0 · · · br 0 · · · 00 0 · · · 0 0 · · · 0...
.... . .
...... . . .
...0 0 · · · 0 0 · · · 0
︸ ︷︷ ︸
(FBB)2Ns×Ns
, (40)
CE (θ) = − 1
θTln
(E
{e−θTB
(log
(SNRBS
Ns
)+log
(rΠ
i=1
(Ns
SNRBS+f2
i λ2i
)))})
= − 1
θTln
e−θTB log
(SNRBS
Ns
)E
(elog
(rΠ
i=1
(Ns
SNRBS+f2
i λ2i
)))−θTB
= − 1
θTln
(e−θTB log
(SNRBS
Ns
)E
{(r
Πi=1
(Ns
SNRBS+ f2
i λ2i
))− θTBln(2)
}). (42)
Based on the method in [28], the optimal equivalent
precoding matrix Feq is composed of FRF and FBB ,
which are designed in (40) with
bj =1
2max
16i6M|fi,j | , (40.1)
ϑi,(2j−1) = ]fi,j − cos−1 |fi,j |2bj
, (40.2)
ϑi,2j = ]fi,j + cos−1 |fi,j |2bj
, (40.3)
in which fi,j is the element of Feq located at the ith row
and the jth column,]fi,j is the corresponding angle.
Based on the result in (40), the number of RF chains
2Ns can satisfy the requirement of the optimal equivalent
precoding matrix. In general, the number of antennas M is
larger than the number of RF chains 2Ns in 5G massive
MIMO wireless systems. Hence, our proposed optimal
equivalent precoding matrix can save the number of RF
chains M − 2Ns.
3.3. Effective Capacity with Mutual CouplingEffect
From [33], we define the effective capacity under
multimedia constraints as
CE (θ) = − 1
θTln(E{e−θTBR}
), (41)
in which θ and B denote the QoS statistical exponent and
bandwidth respectively, E{·} is the expectation operation.
Without losing generality, we consider independent fading
channels that keep static within a frame duration T .
Considering the maximum available rate in (32), (41)
can be extended as (42), and it is clear that f (x) =
x−a, (a > 0) is a convex function. Then an upper bound
of the effective capacity can be obtained using Jensen’s
inequality,
CE (θ) = − 1
θTln(E{e−θTBR
})6 − 1
θTln(e−θTBE{R}
)= BE {R}
. (43)
Based on (32), the upper bound of the maximum available
rate is derived in (44). When the optimal equivalent
precoding matrix is used for massive MIMO wireless
systems, the upper bound of the maximum available rate is
8 Wirel. Commun. Mob. Comput. 0000; 00:1–14 c⃝ 0000 John Wiley & Sons, Ltd.
DOI: 10.1002/wcm
Prepared using wcmauth.cls
Xiaohu Ge et al. 5G Multimedia Massive MIMO Communications Systems
E {Rmax} = E
{r log
(SNRBS
Ns
)+ log
(r
Πi=1
(Ns
SNRBS+ f2
i λ2i
))}6 r log
(SNRBS
Ns
)+
r∑i=1
log
(E
{Ns
SNRBS+ f2
i λ2i
}) , (44)
E{Rmax} 6 r log
(SNRBS
Ns
)+
r∑i=1
log
Ns
rE
λ2
iNs + λ2i
r∑i=1
1λ2i
SNRBS
6 r log
(SNRBS
Ns
)+
r∑i=1
log
(Ns
r2
(Ns +
r
SNRBS
)E
{r∑
i=1
λ2i
})
= r log
(SNRBS
Ns
)+
r∑i=1
log
(Ns
r2
(Ns +
r
SNRBS
)E{tr(H†HAKK†A†
)}), (45)
E{Rmax} 6 r log
(SNRBS
Ns
)+ r log
(Ns
r2
(Ns +
r
SNRBS
)(tr(AKK†A†
)+ E
{tr(H†H
)}))= r log
(SNRBS
Ns
)+ r log
(Ns
r2
(Ns +
r
SNRBS
)(tr(AKK†A†
)+ Pr
)) , (46)
CE (θ) 6 B
(r log
(SNRBS
Ns
)+ r log
(Ns
r2
(Ns +
r
SNRBS
)(tr(AKK†A†
)+ Pr
))). (47)
further derived in (45). Considering the lemma 2.9 in [34],
the upper bound of the maximum available rate is finally
expressed in (46). As a consequence, the upper bound of
the effective capacity in 5G multimedia communication
systems is given by (47).
4. NUMERICAL RESULTS ANDANALYSIS
In this section, we demonstrate the performance of
the multimedia oriented massive MIMO communication
systems in terms of the receive diversity gain as well as the
effective capacity, where both effects of the QoS statistical
exponent and mutual coupling are evaluated. For ease of
illustration, we consider a rectangular antenna array with
the length-width ratio of a/b = 2. There are altogether
128 dipole antenna elements in the rectangular antenna
array [29], each with length and diameter of 0.5λ and
0.001λ, respectively. Then, a reasonable minimum antenna
spacing is dmin = 0.1λ. The large scale fading factor is
normalized to β = 1 [25, 26, 31], with a load impedance
at each antenna as ZL = 50 Ohms [30]. Without loss
of generality, we assume that the BS is located in rich
scattering environment where the incident directions can
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 236
38
40
42
44
46
48
50
52
54
56
Antenna distance d(×λ )
Ante
nna s
pacin
g r
eceiv
e d
ivers
ity g
ain
(dB
)
SNR_BS=5dB
SNR_BS=10dB
SNR_BS=20dB
Figure 2. Antenna spacing receive diversity gain with respect tothe antenna spacing considering different SNRs.
arrive at an arbitrary angle uniformly. Thus it is reasonable
to assume that the elevation angle θ and azimuth ϕq follow
i.i.d. uniform distributions within [−π/2, π/2]. For ease of
demonstration, the default number of independent incident
directions P = 70 is configured, with frame duration T =
1ms and bandwidth B = 1MHz [35].
In Fig. 2, the antenna spacing receive diversity gain Gd
with respect to the antenna spacing is investigated. Mmin
is configured as 1. When the antenna spacing d is fixed,
Wirel. Commun. Mob. Comput. 0000; 00:1–14 c⃝ 0000 John Wiley & Sons, Ltd. 9DOI: 10.1002/wcm
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5G Multimedia Massive MIMO Communications Systems Xiaohu Ge et al.
0 200 400 600 800 1000 1200 140020
25
30
35
40
45
50
55
60
65
70
Antenna number M
Ante
nna n
um
ber
receiv
e d
ivers
ity g
ain
(dB
)
SNR_BS=5dB
SNR_BS=10dB
SNR_BS=20dB
Figure 3. Antenna number receive diversity gain with respect tothe antenna number considering different SNRs.
0 50 100 150 200 250 3000.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
Antenna number M
Eff
ective c
apacity (
bits/s
)
SNR_BS=5dB
SNR_BS=10dB
SNR_BS=20dB
Figure 4. Effective capacity with respect to the antenna numberconsidering different SNRs.
the antenna spacing receive diversity gain increases with
the increase of SNR. But if we fix the SNR at the BS,
it is shown that there is almost no correlation between
the antenna spacing receive diversity gain and the antenna
spacing.
Fig. 3 illustrates the correlation between GM and
the antenna number considering different SNRs. dmin is
configured as 0.1λ. And it is shown that the antenna
number receive diversity gain has a positive correlation
with the antenna number and SNR.
In Fig. 4, the effective capacity is illustrated with
varying values of the antenna number and SNR. For ease of
illustration, the antenna spacing is set as 0.5λ and θ is set
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2x 10
7
Antenna spacing d(×λ)
Eff
ective c
apacity (
bits/s
)
q=10-3
q=10-2.5
q=10-2
Figure 5. Effective capacity with respect to the QoS statisticalexponent θ and the antenna spacing.
0 50 100 150 200 250 3000.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2x 10
7
Antenna number M
Shannon c
apacity (
bits/s
)
Feq_SNR_BS=5dB
Feq_SNR_BS=10dB
Feq_SNR_BS=20dB
ZF_SNR_BS=5dB
ZF_SNR_BS=10dB
ZF_SNR_BS=20dB
Figure 6. Shannon Capacity with respect to the antennanumber considering different precoding matrices.
as 0.01. With a fixed SNR value, it is observed that a higher
effective capacity is obtained by increasing the antenna
number. In addition, with a fixed number of antennas, a
higher effective capacity is obtained with a higher SNR.
Fig. 5 shows the effective capacity with varying values
of QoS statistical exponent and the antenna spacing. With a
fixed antenna spacing, it is observed that a higher effective
capacity is reached by decreasing the QoS statistical
exponent. On the other hand, for a fixed QoS statistical
exponent and increasing of antenna spacing, the effective
capacity almost keeps stationary.
When the number of user and the baseband data
stream are configured as one, Fig. 6 compares the
10 Wirel. Commun. Mob. Comput. 0000; 00:1–14 c⃝ 0000 John Wiley & Sons, Ltd.
DOI: 10.1002/wcm
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Xiaohu Ge et al. 5G Multimedia Massive MIMO Communications Systems
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.011.4
1.5
1.6
1.7
1.8
1.9
2
2.1x 10
7
QoS statistical exponent q
Eff
ective c
apacity (
bits/s
)
EC_SNR_BS=5dB
EC_SNR_BS=10dB
EC_SNR_BS=20dB
EC_upper_bound_SNR_BS=5dB
EC_upper_bound_SNR_BS=10dB
EC_upper_bound_SNR_BS=20dB
Figure 7. Effective capacity with respect to the QoS statisticalexponent θ considering different SNRs.
Shannon capacity with respect to the antenna number
considering different precoding matrices. the proposed
optimal equivalent precoding matrix labeled as “Feq”
and the zero-forcing precoding matrix labeled as “ZF”
are compared in Fig. 6. When the number of antennas
and the SNR are fixed, the Shannon capacities with
the proposed optimal equivalent precoding matrix are
greater than the Shannon capacities with the zero-forcing
precoding matrix. Moreover, the Shannon capacities with
the proposed optimal equivalent precoding matrix has
a positive correlation with the the number of antennas.
However, the Shannon capacities with the zero-forcing
precoding matrix almost keeps stationary with the increase
of the number of antennas. This result indicates that our
proposed optimal equivalent precoding matrix can improve
the Shannon capacity, i.e., the available rate in massive
MIMO wireless communication systems.
Fig. 7 analyzes the effective capacity and the upper
bound of effective capacity with respect to the QoS
statistical exponent considering different SNRs, in which
“EC SNR” labels the effective capacity results and
“EC upper bound SNR” represents the upper bound of the
effective capacity results. When the SNR is fixed, there is a
positive correlation between the effective capacity and the
QoS statistical exponent. Moreover, the more the the QoS
statistical exponent decrease, the closer the upper bound of
effective capacity gets to the effective capacity.
When the number of antennas is configured as 128,
Fig. 8 describes the effective capacity with respect to the
0 100 200 300 400 500 600 700 800 900 10001.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3x 10
7
Independent incident directions P
Eff
ective c
apacity (
bits/s
)
SNR_BS=5dB
SNR_BS=10dB
SNR_BS=20dB
Figure 8. Effective capacity with respect to the independentincident directions P considering different SNRs.
number of independent incident directions. When the SNR
is fixed, there is a positive correlation between the effective
capacity and the independent incident directions.
5. CONCLUSIONS
Based on the mutual coupling effect, an optimal
equivalent precoding matrix has been proposed to
maximize the available rate and save the cost of RF
chains for 5G massive MIMO multimedia communication
systems. Considering the requirements of multimedia
wireless communications, the upper bound of the
effective capacity has been derived for 5G massive
MIMO multimedia communication systems with the
QoS statistical exponent constraint. Compared with the
conventional ZF precoding matrix, numerical results show
that the proposed optimal equivalent precoding matrix
can obviously improve the available rate for 5G massive
MIMO multimedia communication systems. In the future
work, taking into account the QoS statistical exponent
constraints, a more efficient signal detection precoding
algorithm is worth exploring towards better performance of
the multimedia massive MIMO communication systems.
Wirel. Commun. Mob. Comput. 0000; 00:1–14 c⃝ 0000 John Wiley & Sons, Ltd. 11DOI: 10.1002/wcm
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5G Multimedia Massive MIMO Communications Systems Xiaohu Ge et al.
ACKNOWLEDGEMENTS
The authors would like to acknowledge the support from
the National Natural Science Foundation of China (NSFC)
under the grants 60872007, 61301128, 61461136004
and 61271224, NFSC Major International Joint Research
Project under the grant 61210002, the Ministry of Science
and Technology (MOST) of China under the grants
2015FDG12580 and 2014DFA11640, the Fundamental
Research Funds for the Central Universities under the
grant 2015XJGH011 and 2013ZZGH009. This research
is partially supported by the EU FP7-PEOPLE-IRSES,
project acronym S2EuNet (grant no. 247083), project
acronym WiNDOW (grant no. 318992) and project
acronym CROWN (grant no. 610524).
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AUTHORS’ BIOGRAPHIES
Wirel. Commun. Mob. Comput. 0000; 00:1–14 c⃝ 0000 John Wiley & Sons, Ltd. 13DOI: 10.1002/wcm
Prepared using wcmauth.cls
5G Multimedia Massive MIMO Communications Systems Xiaohu Ge et al.
Xiaohu Ge is currently a full
Professor with the School of
Electronic Information and Com-
munications at Huazhong Uni-
versity of Science and Technol-
ogy (HUST), China. He is an
adjunct professor with with the
Faculty of Engineering and Infor-
mation Technology at University
of Technology Sydney (UTS), Australia. He received his
PhD degree in Communication and Information Engineer-
ing from HUST in 2003. He has worked at HUST since
Nov. 2005. Prior to that, he worked as a researcher at Ajou
University (Korea) and Politecnico Di Torino (Italy) from
Jan. 2004 to Oct. 2005. His research interests are in the
area of mobile communications, traffic modeling in wire-
less networks, green communications, and interference
modeling in wireless communications. He has published
more than 100 papers in refereed journals and conference
proceedings and has been granted about 15 patents in
China. He received the Best Paper Awards from IEEE
Globecom 2010. Moreover, he served as the guest editor
for IEEE Communications Magazine Special Issue on 5G
Wireless Communication Systems.
Haichao Wang received the
bachelor degree in electronic
science and technology from
Wuhan University of Technology,
Wuhan, China, in 2013, Now
he is working toward the mas-
ter degree in Huazhong Univer-
sity of Science and Technology,
Wuhan, China. His research inter-
ests include the mutual coupling effect in antenna arrays
and optimization of the number of RF chains in antenna
arrays.
Ran Zi (S’14) received the
B.E. degree in Communication
Engineering and M.S. degree in
Electronics and Communication
Engineering from Huazhong Uni-
versity of Science and Technol-
ogy (HUST), Wuhan, China in
2011 and 2013, respectively. He
is currently working toward the
Ph.D. degree in HUST. His research interests include
MIMO systems, millimeter wave communications and
multiple access technologies.
Qiang Li received the B.Eng.
degree in communication engi-
neering from the University of
Electronic Science and Technol-
ogy of China (UESTC), Chengdu,
China, in 2007 and the Ph.D.
degree in electrical and electronic
engineering from Nanyang Tech-
nological University (NTU), Sin-
gapore, in 2011. From 2011 to 2013, he was a Research
Fellow with Nanyang Technological University. Since
2013, he has been an Associate Professor with Huazhong
University of Science and Technology, Wuhan, China.
He was a visiting scholar at the University of Sheffield,
Sheffield, UK from March to June 2015. His current
research interests include future broadband wireless net-
works, cooperative communications, energy harvesting
and wireless power transfer, and cognitive spectrum shar-
ing.
Qiang Ni (M’04-SM’08)
is a Professor and the Head of
Communication Systems Group
at the School of Computing
and Communications, Lancaster
University, InfoLab21, Lancaster,
U.K. Previously, he led the Intel-
ligent Wireless Communication
Networking Group at Brunel Uni-
versity London, U.K. He received the B.Sc., M.Sc., and
Ph.D. degrees from Huazhong University of Science and
Technology, China, all in engineering. His main research
interests lie in the area of future generation communica-
tions and networking, including Green Communications
and Networking, Cognitive Radio Network Systems, Het-
erogeneous Networks, Small Cell and Ultra Dense Net-
works, 5G, SDN, Cloud Networks, Energy Harvesting,
Wireless Information and Power Transfer, IoTs and Vehic-
ular Networks in which areas he had already published
over 120 papers. He was an IEEE 802.11 Wireless Stan-
dard Working Group Voting member and a contributor to
the IEEE Wireless Standards.
14 Wirel. Commun. Mob. Comput. 0000; 00:1–14 c⃝ 0000 John Wiley & Sons, Ltd.
DOI: 10.1002/wcm
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